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What power needs to be added to 10 to give it a value of a million?

Level 7-8 Algebra - Powers

Indices and powers simplify repeated multiplication. Learn square, cube and negative powers, use laws of indices, and solve KS3 problems with confidence.

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Fascinating Fact:

A credit card’s interest can grow exponentially. At 5% per month, the growth factor is 1.05¹² is about 1.795 after one year.

In KS3 Maths, powers (also called indices) help you write repeated multiplication neatly and calculate quickly. You will use the laws of indices to simplify expressions, evaluate numbers like 10ⁿ, and solve problems involving scientific notation.

Key Terms

Index (power): The small number that tells how many times a base is multiplied by itself, e.g., 3⁴ = 3 × 3 × 3 × 3.
Base: The number being multiplied repeatedly in a power, e.g., in 5³ the base is 5.
Negative index: A power that gives a reciprocal, e.g., a^-2 = 1 / a² (for a not 0).

Frequently Asked Questions (Click to see answers)

What are the laws of indices for KS3?

Key rules include: a^m × aⁿ = a^m+n, a^m ÷ aⁿ = a^{m - n} (a not 0), and (a^m)ⁿ = a^mn.

How do I handle negative and zero powers?

Use a⁰ = 1 (a not 0) and a^-n = 1 / aⁿ. For example, 2^-3 = 1/8 and 7⁰ = 1.

What does 10ⁿ mean in standard form?

It’s a power of ten used to scale numbers. For example, 3.2 × 10⁴ = 32,000 and 5.6 × 10^-3 = 0.0056.

Try These Related Quizzes

1 .

If a = 4 and b = 9, which is the smallest number from the following?

a⁴

b³

6a²

9b = 9 x 9 = 81. In a question such as this you have to work out all the answers in order to determine which is correct

2 .

b⁴ - a² = 621. Given that the value of a is 2, what is a possible value of b?

If a = 2 then a² = 4
621 + 4 = 625
Next you have to work out which number to the power of 4 = 625. This might involve some trial and error!

3 .

If x = 3, what is the value of x³ + x⁴ + x⁵?

243

351

27 + 81 + 243 = 351

4 .

What power needs to be added to 10 to give it a value of a million (1,000,000)?

When you are given 10 to the power of something, remember that the power will be the number of zeros that follow the 1. 10² = 100 (2 zeros); 10⁵ = 100,000 (5 zeros)

5 .

What is the easiest way to calculate the value of 16⁹?

16 x 9

9 x 16

16 x 16

Use a calculator

By using a calculator we found the answer was 68,719,476,736. Without a calculator it might have taken us a week to work out!

6 .

If a = 3 and y = 7, what is the answer to 4a(2y²)?

176

761

1,176

6,711

12 x 98

7 .

400 - x³ = 57. What is the value of x?

Experiment with different values for x until you find the number that fits

8 .

If x = 13 and y = 8, what is the answer to x² - (20y + 9)?

169 - 169 = 0

9 .

When a = 11 and b = 15, which of these gives the smallest number?

a² + 18

10b - 11

b² - 86

11a

All the incorrect answers have the value of 139

10 .

If x = y², and x = 9 then what is a possible value of y?

An easy one to reward you for finishing the quiz! Strictly speaking, it should be plus or minus 3

You can find more about this topic by visiting BBC Bitesize - Powers

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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